How to multiply a three digit decimal by a one digit decimal number (for example 0.529 * 0.7):

Place one decimal above the other so that they are lined up on the right side.
Draw a line under the bottom number. Temporarily disregard the decimal points and
multiply the numbers like multiplying a three digit number by a one digit number.

0.529
0.7

Multiply the two numbers on the right side. (9 * 7 = 63). This number is larger
than 10 so place a six above the center column and place three below the
line in the right column.

6
0.529 0.73

Multiply the digit in the top center column (2) by the digit in the center of the right
column (7). The answer (2*7=14) is added to the 6 above the center
column to give an answer of 20. The units place value (0) of 20 is placed below
the line and the tens place value (2) of the 20 is placed above the five.

26
0.529
0.703

The five of the top number is multiplied by the seven of the multiplier
(5*7=35). The two that was previously carried is added and 37 is placed below
the line. At the start we disregarded the decimal places. We must now count up
the decimal places and move the decimal place to its proper location. We have
three decimal places in 0.529 and one in the decimal 0.7 so
we move the decimal four places to the left to give the final answer of 0.3703.